Nanomolecular solid state electrodynamic thruster

ABSTRACT

A solid-state device that is capable of imparting a directional momentum via thermoelectric microelements. High surface area is used to enhance the efficiency of heat transfer. The device can be operated in adiabatic mode in order to minimize thermal emissions.

CROSS REFERENCE

This application is related, and contains references, to U.S.Provisional Application Nos. 61/239,446, filed Sep. 3, 2009, 61/264,778,filed Nov. 27, 2009, and 61/296,198, filed Jan. 19, 2010, and PCTInternational Application No. US2010/002428, filed Sep. 3, 2010, theentire contents of which are hereby incorporated by reference herein.

TECHNICAL FIELD

The present disclosure relates to methods and apparatus for causing themovement of fluids, for example gases, which may be applied topropulsion systems, vacuum generation, gas compression, and other uses.

BACKGROUND

Devices for the movement of gases are widely utilized. The very firstaircraft engines were piston driven propellers. They worked by couplinga piston engine to a propeller. Their simplicity lead to widespreadadoption until jet engines were invented. Turbojet engines work by theprinciple of coupling a turbine to a fuel combination system. Spinningof the turbine compresses a fuel-air mixture which, when burned,provides thrust and torque to rotate the turbine. The first turbojetengines derived their thrust from exhaust leaving the engines. Modernvariants of the turbojet engines include turbo prop and turbofanengines, which use torque generated by the exhaust to drive a propelleror fan in addition to compressing the fuel-air mixture. Rocket enginesare possibly one of the oldest mechanical propulsion systems, and havenot changed much since their inception. A rocket comprises a tube orcone in which sits (or into which is fed) a fuel oxidizer mixture.Expanding gas from combustion of this mixture creates thrust. Rockets,while offering the highest fuel-thrust ratio of any existing propulsionsystems, cannot easily vary the amount of thrust they generate. Evenadding an ability to turn a rocket on or off significantly complicatesits design.

Adhesion between two materials may be characterized into five types:mechanical, chemical, dispersive, electrostatic, and diffusive. Out ofthese five types, so far, only electrostatic and certain types ofmechanical adhesion are easily reversible processes. Vacuum may be usedto adhere surfaces and lift materials. However, such devices generallyrequire separate mechanisms for generating a reduced pressure andapplying the vacuum to a surface. A vacuum generating system willgenerally include a vacuum pump, control valve, air filter, vacuumgauge, vacuum reserve tank and power source. A benefit of using vacuumfor adhesion, however, is that no residue is left. Typically, the othertypes of adhesion will usually leave behind a residue that is oftenundesired.

Generally, the conventional propulsion systems mentioned above can alsobe used to compress gas. It is also possible to compress gas via theideal gas law, such as in piston or diaphragm pumps. Current devicesgenerally require pumping apparatuses separate from a pressurizedvessel.

The ability of temperature differential to drive gas flow at a surfacehas long been known. In 1873, Sir William Crookes developed a radiometerfor measuring radiant energy of heat and light. Today, Crookes'sradiometer is often sold as a novelty in museum stores. It consists offour vanes, each of which is blackened on one side and light on theother. These are attached to a rotor that can turn with very littlefriction. The mechanism is encased inside a clear glass bulb with most,but not all, of the air removed. When light falls on the vanes, thevanes turn with the black surfaces apparently being pushed by the light.

Crookes initially explained that light radiation caused a pressure onthe black sides to turn the vanes. His paper was refereed by James ClerkMaxwell, who accepted the explanation as it seemed to agree with histheories of electromagnetism. However, light falling on the black sideof the vanes is absorbed, while light falling on the silver side isreflected. This would put twice as much radiation pressure on the lightside as on the black, meaning that the mill is turning the wrong way forCrooke's initial explanation to be correct. Other incorrect explanationswere subsequently proposed, some of which persist today. One suggestionwas that the gas in the bulb would be heated more by radiation absorbedon the black side than the light side. The pressure of the warmer gaswas proposed to push the dark side of the vanes. However, after a morethorough analysis Maxwell showed that there could be no net force fromthis effect, just a steady flow of heat across the vanes. Anotherincorrect explanation that is widely put forward even today is that thefaster motion of hot molecules on the black side of the vane provide thepush.

The correct explanation for the action of Crookes radiometer derivesfrom work that Osborne Reynolds submitted to the Royal Society in early1879. He described the flow of gas through porous plates caused by atemperature difference on opposing sides of the plates which he called“thermal transpiration.” Gas at uniform pressure flows through a porousplate from cold to hot. If the plates cannot move, equilibrium isreached when the ratio of pressures on either side is the square root ofthe ratio of absolute temperatures. Reynold's paper also discussedCrookes radiometer. Consider the edges of the radiometer vanes. The edgeof the warmer side imparts a higher force to obliquely striking gasmolecules than the cold edge. This effect causes gas to move across thetemperature gradient at the edge surface. The vane moves away from theheated gas and towards the cooler gas, with the gas passing around theedge of the vanes in the opposite direction. Maxwell also refereedReynolds' paper, which prompted him to write own paper, “On stresses inrarefied gases arising from inequalities of temperature.” Maxwell'spaper, which both credited and criticized Reynolds, was published in thePhilosophical Transactions of the Royal Society in late 1879, appearingprior to the publication of Reynold's paper. See, Philip Gibbs in “ThePhysics and Relativity FAQ,” 2006, atmath.ucr.edu/home/baez/physics/General/LightMill/light-mill.html.

Despite the descriptions by Reynolds and Maxwell of thermally driven gasflow on a surface dating from the late 19th century, the potential formovement of gases by interaction with hot and cold surfaces has not beenfully realized. Operation of a Crookes radiometer requires rarefied gas(i.e. a gas whose pressure is much less than atmospheric pressure), andthe flow of gas through porous plates does not yield usable thrust,partially due to the thickness and due to the random arrangement ofpores in the porous plates.

SUMMARY

An apparatus operable to propel a gas is described. In some embodiments,the apparatus comprises a plurality of layers arranged in a stack and ameans of heating and/or cooling adjacent layers to form alternating hotand cold layers, and at least one through hole in the stack. In someembodiments, each hot layer is hotter than the immediately adjacent coldlayers and each cold layer is colder than the immediately adjacent hotlayers. A surface of each hot layer is exposed in an interior of thethrough hole, and a surface of each cold layer is exposed in theinterior of the through hole.

In other embodiments, the apparatus comprises at least a first andsecond layer and a means of heating and/or cooling adjacent layers toform alternating hot and cold layers, and at least one hole through thehot and cold layers. Preferably, each hot layer has a chamfer facinginward and in a first direction. An angle between the chamfer of eachhot layer and a center axis of the through hole is designated θ₂. Alsopreferably, each cold layer has a chamfer facing inward and in a seconddirection opposed to the first direction. An angle between the chamferof each cold layer and the center axis of the through hole is designatedθ₁. In some embodiments, the sum of θ₁ and θ₂ falls in the range fromabout 85° to 95°.

BRIEF DESCRIPTION OF THE DRAWINGS

The present methods, devices and systems will now be described by way ofexemplary embodiments to which the invention defined by the claimsappended hereto are not limited. The details of one or more embodimentsof the disclosure are set forth in the accompany drawings and thedescription below. Other features, objects, and advantages will beapparent from the description and the drawings, and from the claims.

FIG. 1 shows a heat pump. This can be a Peltier slab, a slab driven bythermionic emission, or any other suitable means.

FIG. 2 shows gas flow patterns around the heat pump of FIG. 1.

FIG. 3 shows a gas confined in a square box with parallel hot walls andparallel cold walls.

FIG. 4 shows net forces on a stack of Nano Molecular Solid-stateElectrodynamic Thrusters (“NMSET”) with sawtooth geometry.

FIG. 5 shows gas particle velocities around a stack of NMSET withsawtooth geometry.

FIG. 6 shows the thermo-tunneling enhanced Peltier effect.

FIG. 7 shows a stack of NMSET with a parabolic geometry.

FIG. 8 shows gas flow patterns around the stack of NMSET of FIG. 7 andthe momentum space of the gas.

FIG. 9 shows a stack of NMSET with a triangular geometry.

FIG. 10 shows the momentum space of the gas around the stack of NMSETwith a triangular geometry.

FIG. 11 shows a stack of NMSET with a sawtooth geometry.

FIG. 12 shows the momentum space of the gas around the stack of NMSETwith a sawtooth geometry.

FIG. 13 shows a cross sectional view of an NMSET with an internalarrangement of solid state heat pumps. These heat pumps can be driven byPeltier effect, thermionic emission, or any other suitable means.

FIG. 14 shows a perspective view of NMSET with an internal solid stateheat pump arrangement on FIG. 13.

FIG. 15 shows a perspective view of an NMSET with an external solidstate heat pump arrangement.

FIG. 16 shows a cross sectional view of NMSET with an external solidstate heat pump arrangement of FIG. 15.

FIG. 17 shows a perspective view of NMSET with an external non-solidstate heat pump arrangement.

FIG. 18 shows a cross sectional view of a staged NMSET arrangement.

FIG. 19 shows NMSET with a straight geometry.

FIG. 20 shows an exemplary method of manufacturing NMSET.

FIG. 21 shows another exemplary method of manufacturing NMSET.

DETAILED DESCRIPTION Overview

In preferred embodiments, one example of distributed thrusters, is anapparatus described herein that may be referred to as a Nano MolecularSolid-state Electrodynamic Thruster (“NMSET”). The basis of operation ofNMSET makes it possible to apply NMSET in the fields of, for example,propulsion, adhesion, compression and refrigeration, depending on themanner in which an NMSET is employed. In preferred embodiments, NMSETand related distributed thrusters devices provide lightweight, compact,energy-efficient creation of a gas pressure differential with adjustableflow velocity.

Propulsion

In some embodiments, distributed thrusters such as NMSET can offer oneor more of the following improvements in the field of gas propulsion:

1. Improved Resiliency: Damage to any area in a conventional gaspropulsion system would probably lead to system-wide failure.Distributed thrusters provide enhanced redundancy and robustness.2. Lightweight: Electrically driven distributed thrusters, may make useof photovoltaic thin films, in which case fuel load vanishes.Furthermore since each thruster in a distributed thrusters systemcreates a local gas pressure difference, this local effect may requirefewer and or lighter apparatuses to maintain the structural integrity ofsuch gas propulsion system, than what would be normally required in anon-distributed gas propulsion system that generates the same gas flowvolume.3. Scalability: Conventional gas propulsion systems cannot be easilyscaled: optimal turbojets for small aircrafts are not scale reductionsof optimal turbojets for large aircrafts. Distributed thrusters areeasier to scale as scaling primarily changes the quantity of thrusterswhile leaving the individual thruster dimensions mostly intact.4. Response Time: Less massive thrust producing devices spool up anddown faster; as such, thrust from a distributed thruster gas propulsionsystem can be more easily adjusted in response to changes of need.5. Power Independence: Most conventional propulsion systems require aspecific type or class of fuels in order to operate, whereas someembodiments of distributed thrusters, such as, for example, NMSET, onlyrequires a source of temperature differential, which can generated byelectricity.6. Green Propulsion: Some embodiments of distributed thrusters, such asseveral embodiments of NMSET, expect an electrical input and as such, donot require fossil fuels to operate; therefore they do not producepolluting exhaust (e.g. carbon monoxide, nitrogen oxide) during ordinaryoperation when they use a non-polluting method of generating therequired electrical currents.

Adhesion

In some embodiments, distributed thrusters, such as, for example, NMSET,may be used as a lightweight mechanical adhesive that adheres to asurface through suction. The process can be reversible, as the only steprequired to reverse the adhesion is to cut power to the system in someembodiments. Using such a system can provide further benefit overelectrostatic adhesion in that such a system does not require a materialto be adhered to be flat or conductive, and does not leave behindresidue. Compared to other mechanical adhesion processes, using such asystem may not require a surface being adhered to be pretreated.

Gas Compression

Because distributed thrusters, such as, for example, NMSET, can bearranged to drive gas flow through a surface, all or part of apressurized vessel may function to provide gas compression. Thus, insome arrangements, separated pumping and pressurized containment may notbe required. Moreover, because, the action of such a system generallyoccurs over a short distance, it is possible, in some embodiments, touse such a system as a highly compact compressor by stacking multiplestages of distributed thrusters. Conventional gas propulsion systemsgenerally operate over length scales of centimeters and sometimesmeters. Thus, stacking conventional propulsion systems tends to be acomplex and expensive proposition. By contrast, distributed thrusterscan be packaged to operate over smaller scales, down to, for example,micrometers. Furthermore, the versatility of such systems means thatsuch a system can be readily adapted to function as a high-pressurepump, a standard atmospheric pump, or with a sufficient number ofstages, as a high vacuum pump.

NMSET Design

In one aspect and embodiment, NMSET and some related devices describedhere may be thought of as functioning by reducing entropy in gas incontact with the system. Optionally, such device may add energy, inaddition to the energy lost through inefficiencies in the system, e.g.thermal energy, to the gas. In another aspect and embodiment, thegeometry of NMSET and some related devices can affect gas flow directionand convenience of use. Several embodiments of NMSET and some relateddevices may be further distinguished from previous thermal transpirationdevices and the like by the combined application of scale parameters,materials having advantageous molecular reflection properties,geometries, design, construction and arrangement of elements thatprovide significant increase in efficiency, and or capabilities tooperate at higher ambient pressures and/or produce higher flow rates.Described herein are various exemplary embodiments of NMSET withdiscussion of these and other parameters that, in preferred embodiments,can create a strong gas flow in a particular direction with minimalthermodynamic loss, and or operate at higher ambient pressures and orproduce higher flow rates.

Reduction of entropy in a gas by NMSET may be represented by atransformation A in the momentum space k of the gas. A can be expressedin a matrix once a set of suitable bases is chosen for the momentumspace k. If the expectation value of the transformed momentum space Akis nonzero, the NMSET receives a net momentum in the opposite directionof the expectation value due to the conservation of momentum.

The geometry of NMSET may be optimized for more efficient functioning.The geometry of NMSET affects the transformation matrix A. A geometrythat produces a matrix A essentially equal to an identity matrix l doesnot create a net momentum bias (i.e. will not make the transformedmomentum space Ak have a nonzero expectation value). Rather, gasvortexes may be generated. Geometries that result in larger eigenvaluesof A tend to imply a more efficient function, e.g., that more momentumis carried by gas particles moving in a particular direction.

As an example, consider a heat pump 100 immersed in a gas, shown inFIG. 1. The heat pump 100 comprises an upper layer 101 and a lower layer102. For simplicity, a Cartesian coordinate system can be referencedwith a y-axis pointing from the lower layer 102 to the upper layer 101.A temperature differential can be established by a Peltier device (notshown) between the layers or any suitable means such that the upperlayer 101 is colder than the gas and the lower layer 102 is hotter thanthe gas. For sake of simplicity, one may assume that the heat pump 100has 100% Carnot cycle efficiency. However, other efficiencies arecontemplated. In this case, the heat pump 100 will not transfer net heatinto the gas. Transformation caused by the heat pump 100 to the momentumspace k of the gas can be expressed by a Hermetian matrix A. When a gasparticle (molecule or atom) collides with the lower layer 102, assumingthe collision is diabatic, the gas particle rebounds off at a highervelocity than before the collision. When a gas particle collides withthe upper layer 101, assuming the collision is diabatic, the gasparticle rebounds off the upper layer 101 at a reduced velocity thanbefore the collision. The heat pump 100 feels a net force in the ydirection. In other words, the lower layer 102 heats and thus increasespressure of the gas below the lower layer 102, while the upper layer 101cools and thus decreases the pressure of the gas above the upper layer101. The pressure difference exerts a force on the heat pump 100 in they direction. In terms of transformation of the momentum space k of thegas, as gas particles rebounding from the upper layer 101 leave withless momentum than gas particles rebounding from the lower layer 102,the transformed momentum space Ak becomes skewed preferentially in the−y direction, i.e., the expectation value p of the transformed momentumspace Ak is nonzero and points to the −y direction. Assuming the gas andthe heat pump 100 compose a closed system (i.e., no interaction withother objects), the heat pump 100 gains a momentum −p to conserve thetotal momentum of the closed system.

While the geometry of the heat pump 100 in FIG. 1 does generate adirection force, in certain circumstances it may not be practical forthe following reasons:

1. If the heat pump 100 is large, translational motion of the heat pump100 along the y direction forces the gas to flow all the way aroundedges of the heat pump.2. The vast majority of the heat is transferred from surfaces of theheat pump 100 via gas convection.3. Gas near the surfaces has an insulating effect. Momentum transferbetween the heat pump 100 and the gas is not efficient except inproximity of the edges of the slab, as shown in FIG. 2.4. Surface area of the heat pump 100 is surface area of its convex hull.

These problems all relate to a single core issue, very little of the gashas any direct surface contact. Thus, a more complex geometry can beadvantageous. Exemplary embodiments with three different geometries aredescribed herein.

Principles of Operation

Although many different geometries of NMSET or related devices arepossible, the principle of operation of NMSET remains the same. Whilenot wanting to be limited to any particular theory, operation usesenergy to reduce entropy on some device surfaces and transfer reducedentropy to a gas in contact with the surface. The device can optionallydonate energy to the gas by raising the gas temperature. The function ofNMSET may be therefore divided into three areas: the means by whichentropy on surfaces of the device is reduced, the means by which thereduced entropy is transferred to the gas, and the optional means otherthan the inefficiency of the Carnot cycle of the heat pump by which thegas temperature is increased.

Temperature Differential

A temperature differential between layers of material or more precisely,between two opposing surfaces is generally required for NMSET or relateddevice to operate. In preferred embodiments described herein, atemperature differential can be established in a solid-stateelectrodynamic mechanism, i.e., the “SE” of NMSET. However, the devicesand methods described here are not limited to electronic or purely solidstate devices. For example, a temperature differential may beestablished by conduction of heat from combustion using a fluid coolant,exothermic chemical reaction, or other chemical source. A temperaturedifferential may be established by simple resistive heating, by thePeltier effect, by thermionic emission, by the thermo-tunneling enhancedPeltier effect, or by any other suitable means, such as explained below.A means by which the temperature differential is established between twoobjects can be phenomenologically described by two characteristics:entropy-reduction (heat transfer between the two objects), anddiabaticity (total heat transfer between environment and the twoobjects).

In one embodiment, the Peltier effect can be used to establish atemperature differential. The Peltier effect occurs when an electriccurrent is applied through a loop composed of two materials withdifferent Peltier coefficients joined at two junctions. Depending on thedirection of the electric current, heat flows from one junction to theother, causing a temperature differential to be established between thejunctions. The Peltier effect can be understood as follows: Heatcapacity of charge carriers in a material is characterized by thePeltier coefficient Π, which is the amount of heat carried per unitcharge carriers in the material. When an electric current l flowsthrough a junction of material A with Peltier coefficients Π_(A) andmaterial B with Peltier coefficient Π_(B), the amount heat carried bycharge carriers to the junction in a unit time is l×(Π_(A)−Π_(B)).

An ideal Peltier effect reduces entropy locally and is adiabatic.Assuming Joule heating and or Carnot cycle inefficiencies can beignored, in the Peltier effect, heat is transferred from one junction toanother, but no heat is added into the loop of the two materials. Thisentropy reduction can provide for advantages in the stackability ofNMSET and related devices. Consequently, the Peltier effect lends itselfparticularly well to some embodiments.

In this embodiment, a power source drives an electric current betweentwo surfaces. Charge carriers such as electrons and/or holes carry heatas they flow in the electric current, and thus create a temperaturedifferential between the two surfaces. Entropy is reduced as thetemperature differential is established.

Phonon flow reduces the temperature differential established by thePeltier effect. If phonons are permitted to flow freely (i.e., infinitethermal conductivity or zero heat capacity), their flow will cancel thetemperature differential established by the Peltier effect. Efficiencyof the Peltier effect can be increased by reducing electrical resistanceand thermal conductance.

One way to reduce thermal conductance is to place a narrow vacuum gap inthe path of the electric current. Phonons cannot easily pass the vacuumgap but charge carriers can do so under a voltage across the vacuum gap.This is called thermo-tunneling enhanced Peltier effect (or thermotunnelcooling). FIG. 6 shows a diagram of the thermo-tunneling enhancedPeltier effect. Charge carriers 601 can tunnel through a vacuum gap 602.

The thermo-tunneling enhanced Peltier effect is generally onlysignificant at high temperatures or voltages, unless enhanced by choiceof surface geometry and materials that can restrict behavior of chargecarriers near the vacuum gap and increase tunneling probability. Forexample, suitable surface coatings and structures can function as afilter that do not allow low energy states of charge carriers but onlyhigh energy states of charge carriers near the vacuum gap.

In another embodiment, a temperature differential can be created andmaintained by field-enhanced thermionic emission. Thermionic emission isa heat-induced flow of charge carriers over a potential-energy barrier.The charge carriers can be electrons or ions (i.e., thermions). In asimple approximation, the potential-energy barrier acts like a dam, inthat it withholds carriers with thermal energy less than its height andallows carriers with thermal energy greater than its height to flowover. When the overflowing carriers pass the potential-energy barrier,heat is carried away with them. The carriers left behind thepotential-energy barrier re-thermalize (redistribute in energy) to alower temperature. Thermionic emission typically requires an operatingtemperature of several hundred degrees Celsius so that a non-negligiblefraction of the carriers has thermal energies great enough to overcomethe potential-energy barrier. An electrical field can assist thermionicemission by reducing the height of the potential-energy barrier andreducing the required operating temperature.

A temperature differential in NMSET or related device can also beestablished by using resistive heating (explained below) and/or bysuitable chemical processes. In order to maintain the temperaturedifferential without raising the overall temperature of the device, somecooling means can also be provided, such as a heat sink exposed toatmosphere. No matter what cooling means is used, the temperaturedifferential is more pronounced if warmer surfaces of the device are notcooled as efficiently as cooler surfaces, which can be achieved, forexample, by thermal insulation.

Force Generation

In one aspect, the production of net thrust may be thought of as thetransfer of the reduced entropy from an established temperaturedifferential to a gas. Without wishing to be bound by theory, consider asingle device operating in a gas, as an adiabatic process. In thisexample, a temperature differential between a hot and a cold layer canbe established by a suitable means such as the Peltier effect. Forsimplicity, assume no net heat transfer between the gas and the device.Particles of the gas will impact the hot and cold layers with equalprobabilities, and their interaction with these layers will haveconsequences on local momentum space of the gas near surfaces of the hotand cold layers. The local momentum space of the gas very close to asurface of the hot and cold layers has nonzero expectation value whenthe gas and the surface have different temperatures. Assuming also thatno gas particles penetrate the surface, the gas particles rebound fromthe surface with momenta different from their incident momenta, whichskews the momentum space along the surface normal, and the magnitude ofthe skew is directly related to the temperature difference between thesurface and the gas.

In an arrangement with random geometry (i.e. surface normals atdifferent surface locations point to random directions), the weightedsum of expectation values of local momentum spaces of the gas is nearlyzero, which results in almost no net thrust. In NMSET with an optimizedgeometry, however, the weighted sum of expectation values of localmomentum spaces of the gas can be non-zero, which leads to a net thrust.

A trivial example of an arrangement that has non-zero net thrust isshown in FIG. 1, as described above. This geometry is not very efficientbecause macroscopic convective gas flows and vortex formation increasethe entropy and limit the amount of useful work. Exemplary convectivegas flows 120, 130 are shown in FIG. 2. Gas at ambient temperature 110flows towards the cold layer 101 and gets cooled. Cooled gas flows 120away from the cold layer 101 and around the edge of the heat pump 100towards the hot layer 102. Heated gas flows 130 away from the hot layer102.

To simplify the description, it may be helpful to think about the systemin terms of Newton's second law and the kinetic theory of gases. Aroundthe heat pump 100 in FIGS. 1 and 2, assuming that temperature of the gasis bracketed by the temperatures of the layers 101 and 102, gasparticles that collide with the layer 102 leave the layer 102 withgreater momentum than before the collision. Similarly, gas particlesthat collide with the layer 101 leave the layer 101 with lesser momentumthan before the collision. Since gas pressure is directly related tomomenta of gas particles, gas near the layer 102 has higher pressurethan gas near the layer 101. This pressure bias pushes the entire heatpump 100 in the y direction.

In another embodiment, the heat pump 100 can have at least one throughhole between the layer 101 and 102. Gas spontaneously flows from thelayer 101 to the layer 102 through the hole which enables higher heatingrate of the gas. Such preferential flow of gas is referred to as thermaltranspiration. Assuming gas near the layer 101 has temperature of T_(c)and pressure of P_(c), and gas near the layer 102 has temperature ofT_(h) and pressure of P_(h), thermal transpiration causes the gas toflow from the layer 101 to the layer 102 through the hole, if thefollowing equation is satisfied:

$\begin{matrix}{\sqrt{\frac{T_{h}}{T_{c}}} \geq \frac{P_{h}}{P_{c\;}}} & \lbrack 1\rbrack\end{matrix}$

In order to improve efficiency, it is helpful to understand where theclassical limit exists within gas flows. Convective descriptions of gasflow break down at around length scales where the Knudsen numberappears. As a result, in some aspects, the mean free path of a gasbecomes a useful parameter in determining advantageous geometries ofNMSET.

For instance, consider a gas at a particular pressure having a mean freepath of 10 nm. If a cloud of such gas is trapped in a two dimensionalsquare 20 nm by 20 nm box as shown in FIG. 3, a gas particle, within 10nm of travel, will be approximately as likely to have struck another gasparticle as it is to have struck the walls of the box. If the walls ofthe box are heated, then smaller boxes will reach thermodynamicequilibrium with gas therein faster than larger boxes, because gasparticles in smaller boxes have more chances to collide with andexchange heat with the walls. Generally, when most of collisions in agas are between gas particles and a surface, then thermodynamicequilibrium can be achieved approximately in the mean free time (thetime it takes a gas particle to travel the mean free path).

For this reason, in some embodiments, the characteristic scale ofindividual features of NMSET and related devices may be nanoscale, i.e.,the “NM” of NMSET. However, it must be understood that the methods anddevices described here are not limited to nanoscale embodiments. Themean free path parameter is dependent on gas density so that in someembodiments and uses, larger scale features may be employed.Furthermore, as described herein, pluralities of NMSET and relateddevice elements can be combined to provide action over a large surface.For example, distributed thrusters such as NMSET may advantageously bearranged in arrays and or arrays of arrays to provide directed movementof gas over across large surfaces, for example, as illustrated in FIGS.15, 16 and 17. Distributed thrusters such as NMSET can also be arrangedin one or more stages to achieve a greater pressure differential, forexample as illustrated in FIGS. 18A-18D. FIG. 18A illustrates a crosssectional view of an array of staged distributed thrusters such as NMSETarrangements 1800. Each staged arrangement 1800 is composed of stages1810, 1820, 1830 of in the form of concentric half-spheres containingarrays of distributed thrusters such as NMSET 1840, 1850, 1860illustrated in blow-up in FIGS. 18B-18D. Individual distributed thrusterapertures 1845, 1855, 1865 in each stage increase in optimal size andthickness in accordance with the decreasing ambient pressure that wouldbe experienced at each previous stage in operation.

Surface Interaction

Interaction between surfaces can affect the momentum spacetransformation matrix A. If nearby surfaces can easily exchange phononsvia gas particles, then the entropy at these surfaces will locallyincrease at a higher rate than surfaces which cannot easily exchangephonons via development of vortexes. This will generally reduce theefficiency of a system.

One method by which phonon exchange may be reduced is to limit oreliminate any shared bases between surfaces. For instance, consider gasparticles in the box 300 in FIG. 3. Box 300 comprises two planar hotwalls 302 parallel to each other, and two planar cold walls 301 parallelto each other and perpendicular to the hot walls 302. If the box 300 iscomparable in size to the mean free path of the gas particles thereinand the walls 301 and 302 are perfectly specular, the gas particles canreach thermal equilibrium with the cold walls 301 and the hot walls 302independently. This is because surface normals of the walls are onlyshared between the two cold walls 301 or between the two hot walls 302,but not between a cold wall 301 and a hot wall 302. Consequently, littleto no momentum can be exchanged between the hot walls 302 and the coldwalls 301 by the gas particles. This is because interaction between thegas particles and the cold walls 301 only affect momenta in the xdirection but not momenta in the y direction; and interaction betweenthe gas particles and the hot walls 302 only affect momenta in the ydirection but not momenta in the x direction and the fact that momentain the x direction are orthogonal with momenta in the y direction,assuming no collisions between gas particles. After thermal equilibriumis reached between the gas particles and the walls, the gas particlesmove faster in the y direction than in the x direction.

As a practical matter, surfaces are usually not perfectly specular.However, specular surface properties exist very strongly in somematerials so that there are angles for which convective flows in cornersmay be reduced. This effect is generally observed when the Knudsennumbers are large, which is a preferred condition for NMSET and relateddevices, particularly in nanoscale embodiments. The Knudsen number (Kn),named after Danish physicist Martin Knudsen (1871-1949), is adimensionless number defined as the ratio of the molecular mean freepath to a representative physical length scale. In NMSET or the relateddevices discussed here, the representative physical length scale istaken to be the order of magnitude of the aperture diameter of thedevice, i.e., the representative physical scale length is, for example,a nanometer if the aperture is measured in nanometers, and a micrometerif the aperture is measured in micrometers. In preferred methods ofusing the devices disclosed herein the Knudsen number is preferablygreater than 0.1, or greater than 1, or greater than 10.

Methods of Optimizing NMSET and Related Devices

Modeling

Performance of NMSET with a specific geometry can be simulated by aMonte-Carlo method for optimization. Specifically, a simulation forNMSET or related device with any given geometry starts with a group ofgas particles with random initial positions and momenta around thedevice. Positions and momenta of these particles after a small timeinterval are calculated from the initial positions and momenta, usingknown physical laws, parameters such as temperature, pressure, chemicalidentity, geometry of the device, interaction between surfaces of thedevice and the gas particles. The simulation is run through a chosennumber of iterations and simulation results are analyzed. The geometryof the device can be optimized using simulation results. In preferredembodiments, a device is constructed using the results of the simulationanalysis.

In a preferred embodiment, a simulation can be represented in thefollowing table:

Algorithm 1 EVOLVE MODEL(M, P, k) M←0 P←a set of search parametersk←number of iterations for i = 1 to k do V←An instance of P V←Vperturbed by M E←MONTE CARLO(V) Update M using E end for

A perturbation model M is evolved through a number (k) of iterations.First,

M is initialized to an empty set, indicating no solution knowledge.Then, a loop is started in which the search parameters generate anarbitrary element from the definite search space P and the prior learnedknowledge M is used to perturb P. The specific algorithm used to perturbas an implementation detail.

If run in a grid computing environment, M should ideally be identicalamong all nodes, but this is not necessary due to the inherentlystochastic nature of the process. The step of EVOLVE_MODEL whichactually runs the Monte-Carlo simulation is the most computationallyexpensive of all by far and offers a lot of time to synchronize M.

Specific parameters depend on the environment. The parameters that theuser can specify include the following:

1. Molecular diagrams, in some embodiments containing up to three atoms,such as CO₂ or H₂O.2. Partial concentrations for constituent molecules.3. Initial temperature and pressure of the entire gas.

In a stationary simulation, the Monte-Carlo simulation can be run withperiodic bounds in all axes. In the y axis, however, particlesencountering the periodic bound are stochastically thermostattedaccording to temperature and pressure settings in order to simulateambient conditions. In the x axis, particle velocities are unmodified inorder to simulate a periodic ensemble of identical device assembliesalong that direction. The simulation may be run in two dimensions toreduce the computational complexity of the simulation. A threedimensional simulation should give similar results where the modeleddevice has cylindrical symmetry. Note that in general, a simulator doesnot have to use the periodicity as indicated here and may not specifyany boundaries at all; they are only defined as a computationalconvenience.

In preferred embodiments, potential device geometries can be evaluatedin consideration of the conditions under which a device will be used andknown surface reflection properties of the material from which it willbe constructed. Geometrical parameters can be optimized by analyzingresults from simulation before the geometry is actually used inmanufacture of NMSET and related devices.

Example Geometries

Four embodiments with different geometries are particularly discussedbelow. These four geometries will be referred to as Straight, Parabolic,Triangular, and Sawtooth. It must be noted that the geometries of theNMSET and related devices described here can vary considerably and theseexamples should be taken only as illustrations for the purpose ofdiscussing the effects of certain design choices on system efficiencies.

Straight

FIG. 19 shows an embodiment of NMSET or related device 1900 with astraight geometry. In this embodiment, the device 1900 comprises a hotlayer 1902 and a cold layer 1901. The terms “hot layer” and “cold layer”mean that these layers have a temperature difference therebetween, notthat the “hot layer” is necessarily hotter or the “cold layer” isnecessarily colder, than a gas that NMSET or related device is immersedin. At least one straight through hole 1910 extends through all layersof the device 1900 and preferably has a similar cross-sectional shapeand size for each set of layers. The straight through hole 1910 can haveany cross-sectional shape such as circular, slit, and comb.

Preferably, a total length 1910L (i.e. a distance from one entrance tothe other entrance) of the straight through hole 1910 is up to 10 times,up to 5 times or up to 2 times of the mean free path of a gas in whichthe device 1900 is immersed. The mean free path of air at the standardatmosphere pressure is about 55 nm. At higher altitude, the mean freepath of air increases. For atmospheric applications, the total length1910L is preferably not greater than 1500 nm, and depending onapplication more preferably not greater than 550 nm, not greater than275 nm or not greater than 110 nm. A temperature differential betweenthe hot layer 1902 and the cold layer 1901 is preferably at least 0.5°C., more preferably at least 30° C., more preferably at least 50° C.,and most preferably at least 100° C.

The hot layer 1902 and the cold layer 1901 may be separated by a gaptherebetween for thermal isolation. The gap preferably is a vacuum gapand/or contains a thermal insulator. In one example, the gap contains aplurality of thin pillars made of a good thermal insulator such assilicon dioxide.

The device 1900 has preferably at least 10 straight through holes persquare centimeter. A total perimeter length of all the straight throughholes of the device 1900 per square centimeter is preferably at leasttwo centimeters.

Parabolic

FIG. 7 shows an embodiment of an NMSET or related device 700 with aparabolic geometry. In this embodiment, alternating hot layers 702 andcold layers 701 are stacked. In the illustration, each hot layer 702 andcold layer 701 has a straight through hole. All the holes are aligned.The hole in each hot layer 702 has the similar size as the hole in thecold layer 701 immediately above, and is smaller than the hole in thecold layer 701 immediately below. Each cold layer 701 is colder than itsimmediate adjacent hot layers 702 and each hot layer 702 is hotter thanits immediate adjacent cold layers 701. A surface 702 a of each hotlayer 702, which has a surface normal in the −y direction, is exposed.All the holes collectively form a nozzle with a contour of a parabolicsurface. This geometry minimizes shared bases between the hot and coldlayers. However, because NMSET or related device may not substantiallyincrease the energy of the gas, the increasing hole diameter may resultin a drop in gas pressure at the edges. This can create strong vortexesnear the lower aperture, which reduce total efficiency. NMSET with theparabolic geometry can be adiabatic or isobaric, but not both. Anapproximation of gas flow in NMSET or related device with the parabolicgeometry is shown in FIG. 8. The momentum space of the gas is skewedsuch that the expectation value of the momentum points to the −ydirection.

Although the parabolic geometry is effective in NMSET or related device,a drop in gas pressure puts an upper bound on the size of the loweraperture. In general, any adiabatic device in which the gas being movedundergoes a change in volume will suffer in its efficiency.

If the temperature differential in a device with the parabolic geometryis established by a diabatic means (i.e. the device raises the overalltemperature of the gas), then the NMSET with the parabolic geometry maynot suffer in its efficiency from the gas undergoing a change in volume,as long as the amount of heat added to the gas is sufficient to preventthe formation of vortexes. However, such a device suffers in itsefficiency from higher total entropy, i.e., the eigenvectors of themomentum space of the gas are not as far apart if the gas has to expand,but supplying heat at small scales is typically easier than carrying itaway.

Triangular

The triangular geometry detailed in FIG. 9 is a partial optimization ofthe parabolic geometry for adiabatic flows. In this case, the gas is notpermitted to experience a sufficient expansion to trigger large-scalevortex generation. Furthermore, because the apertures do not changesize, a triangular arrangement such as this one may be easily stacked.

The momentum space of this triangular geometry is more efficientlybiased, as is illustrated in FIG. 10. As in the parabolic arrangement,the exposed hot and cold surfaces meet at preferably a 90-degree angle;however, a source of inefficiency arises when particles carry heat backand forth between surfaces across the center gap.

FIG. 9 shows a stack 900 of NMSET or related device with the triangulargeometry. Each device in the stack 900 comprises a hot layer 902 and acold layer 901 of equal thickness. The temperature differential betweenthe cold and hot layers 901 and 902 can be established by any suitablemeans such as the Peltier effect or any other heat pump. Each device hasa through hole 903. Each though hole 903 has approximately a 45° chamfer(9031 and 9032) on each entrance. The surface of the chamfers 9031 and9032 is, for example, from 1.40 to 1.42 times of the thickness of thecold and hot layers 901 and 902, not including modifications to theacute angles for structural considerations. The through holes 903 in alllayers in the stack 900 are aligned. In general, the temperatures of thehot layers 902 in a device in the stack 900 do not increasemonotonically from one side of the stack to the other side. In general,the temperatures of the cold layers 901 in a device in the stack 900 donot decrease monotonically from one side of the stack to the other side.Preferably, each cold layer 901 is colder than its immediate adjacenthot layers 902 and each hot layer 902 is hotter than its immediateadjacent cold layers 901. For engineering reasons, the hot and coldsurfaces of the triangular arrangement may not come to a fine point.

Sawtooth

FIG. 11 shows a stack 1100 of NMSET or related device with a sawtoothgeometry. Each device in the stack 1100 comprises a hot layer 1102 witha thickness of t_(h) and a cold layer 1101 with a thickness t_(c). Thetemperature differential between the cold and hot layers 1101 and 1102can be established by any suitable means such as the Peltier effect orany other heat pump. Each device has a through hole 1103. In theillustrated device, each through hole 1103 has a chamfer 11031 at theentrance on the side of the cold layer 1101, and a chamfer 11032 at theentrance on the side of the hot layer 1102. An angle between the chamfer11031 and a center axis of the through hole 1103 is θ₁; an angle betweenthe chamfer 11032 and a center axis of the through hole 1103 is θ₂. Thesum of θ₁ and θ₂ is preferably from 75° to 105°, more preferably from85° to 95, and more preferably from 88° to 92°. The ratio of t_(c) tot_(h) is substantially equal to the ratio of cotangent of θ₁ tocotangent of θ₂. θ₂ is preferably from 70° to 85°.

The relationships of the chamfer angles described here are preferredlimitations, not hard boundaries. In general for materials exhibitperfectly specular molecular reflection properties, the relationships ofthe chamfer angles can be slightly relaxed. For materials exhibit lessthan perfectly specular molecular reflection properties, therelationships shall be stringent. The chamfer geometries are preferablyarranged so as to minimize shared bases. The surface normals of thespecularly reflecting chamfer surfaces can thus preferably beorthogonal. Deviations from orthogonality can incur a penalty inefficiency as a cosine function. For engineering reasons, the hot andcold surfaces of the sawtooth arrangement may not come to a fine point.

In the illustrated device, the through holes 1103 in all layers in thestack 1100 are aligned. Temperatures of the hot layers 1102 in eachdevice in the stack 1100 do not increase monotonically from one side ofthe stack to the other side. Temperatures of the cold layers 1101 ineach device in the stack 1100 do not decrease monotonically from oneside of the stack 1100 to the other side. Each cold layer 1101 is colderthan its immediate adjacent hot layers 1102 and each hot layer 1102 ishotter than its immediate adjacent cold layers 1101.

The sawtooth geometry shown in FIG. 11 offers an improvement over thetriangular geometry in that all hot layers 1102 are preferably orientedin nearly the same direction (i.e., θ₂ is preferably nearly 90°). Thisreduces direct interaction between hot and cold layers 1102 and 1101across the through hole 1103, and improves overall efficiency.

Furthermore, because the hot layers 1102 have a lower exposed surfacearea than the cold layers 1101, and because the cold layers 1101 arepreferably oriented at a shallower angle relative to the center axis ofthe through hole 1103 than in the triangular geometry, the sawtoothgeometry is capable of reducing the entropy in the gas (and therebycausing it to do more work) more efficiently than the triangulargeometry. The momentum space of this sawtooth geometry is moreefficiently biased than the momentum space of the triangular geometry,as is illustrated in FIG. 12.

In the triangular configuration, device slices on opposite sides of across section have a magnitude of 1/√{square root over (2)} in the yaxis because their separation angle 90 degrees. This limits theefficiency of entropy reduction, as some of the entropy is going to beneutralized in direct inter-surface interaction.

In the sawtooth configuration, however, the hot layers 1102 not onlyshare no basis with the adjacent cold layers 1101, but also share verylittle basis with hot and cold layers across the through hole 1103. Thiscombined property makes the sawtooth geometry more efficient than thetriangular geometry.

After NMSET or related device is powered (i.e. temperature differentialis established), gas particles rebounding from cold layers have areduced net velocity, while gas particles rebounding from hot layershave higher net velocity. FIG. 4 shows net forces the layers of thestack 1100 (sawtooth geometry) experience. In a stable state, lowpressure is generated at the entrance aperture (upper aperture in FIG.4) which in turn generates a corresponding low-pressure region above thestack 1100, and a high-pressure region below the stack 1100. Gasparticle velocities of the stack 1100 resulting from the gas particlecollisions are shown in FIG. 5.

Means for Establishing Temperature Differential

Internal Peltier

According to one embodiment, each element in the device geometry actsboth as a particle director and as the entropy reducer. In a Peltierdevice, the hot and cold plates are made of materials with differentPeltier coefficients. Electrical current is made to flow between thecold and hot plates. This flow of current carries with it Peltier heat,establishing the temperature differential necessary to operate thedevice. In some embodiments, piezoelectric spacers can be disposedbetween device elements to maintain the separation gaps therebetween.

A cross section of NMSET or related device according to an embodimentwith an internal Peltier arrangement is detailed in FIGS. 13 and 14. Allhot layers 1302 are connected. All cold layers 1301 are connected.Electric current flows through a Peltier device interposed between thecold and hot layers to establish a temperature differential. The thinnerthe layers are, the higher the electric current is necessary.

NMSET or related device with the internal Peltier arrangement can makeit easier to reduce the size of the device. A single stack such as theone shown in FIG. 14 can be fully functional to generate thrust. NMSETor related device with the internal heat pump are further suitable foruse in microelectromechanical systems (MEMs) that emphasize the highestdegree of granularity.

Field-Enhanced Thermionic Emission

In another embodiment, the temperature differential can be generated byfield-enhanced thermionic emission. As shown in FIG. 19, an electricalfield can be established between the layers 1901 and 1902 such thatcharge carriers thermally emitted from the cold layer 1901 carry heatfrom the cold layer 1901 to the hot layer 1902.

External Peltier

In another embodiment, the temperature differential can be generated bya heat pump, such as a Peltier device external to NMSET or relateddevice. This Peltier device arranged in a checker board fashion isthermally coupled to NMSET or related device stack 1500 via interfacelayers 1510 and 1520 as detailed in FIGS. 15 and 16.

A device with an external Peltier device has the benefit of separatingthe materials used to generate gas flow from the materials used togenerate the temperature differential. From an engineering standpointthis may be desirable, as the materials suitable for a heat pump may notbe suitable for microstructures, or vice versa. In addition, an externalheat pump can be made larger and more efficient, and may require lesscurrent to establish a sufficient temperature differential.

Piezoelectric spacers can be used between layers. Materials suitable foruse in NMSET preferably are strong enough to mechanically withstandthermal expansion and contraction, and/or preferably have very smallexpansion coefficients. Otherwise, holes in the layers could becomemisaligned, which could reduce efficiency.

External Non-Peltier

According to yet another embodiment, a temperature differential isestablished by any suitable heat source and/or heat sinks. For example,the heat sources might be field-enhanced thermionic emission, resistiveheaters, chemical reaction, combustion, and/or direct illumination ofbright light or other forms of radiation. An illustration of such anembodiment is shown in FIG. 17. In the example shown, a heating surface1702 can be resistive heating material, or a material that canefficiently receive radiative heating. The external non-Peltier heatpump is convenient because it does not require a built in heat pump suchas a Peltier device. For some applications, it may be convenient todirect the heating surface towards a source of radiation, such as thesun, rather than first converting radiation into electricity and drive aheat pump. Alternatively, a source of radiation may be directed toward aheat absorbing surface in thermal communication with the hot layer ofNMSET or related device. In an external non-Peltier heat pump, however,more care is preferably taken to ensure that the NMSET or related devicedoes not overheat.

The capillaries 1750 illustrated in FIG. 17 provide an exemplarymechanism by which a heat sink could be provided; however, it is alsopossible for the heat sink to simply be a series of vanes, or any othersuitable heat sinks. Alternatively, the external non-Peltier heat pumpin FIG. 17 could be configured to provide a heat source through thecapillaries 1750. The heat source can be an exothermic chemicalreaction, preferably one that does not generate too much pressure.

Materials

NMSET and related devices may be constructed of a wide range ofmaterials. In various aspects, properties of materials may be exploitedin combination with desirable geometries.

Specular reflection of gas molecules is a preferred property of thematerials which form the gas-exposed surfaces of NMSET or relateddevice, e.g. the heated and cooled surfaces which are in contact withflowing gas. Specular reflection is the mirror-like reflection of light,or in this case gas particles, from a surface. On a specular surface,incoming gas particles at a single incident angle are reflected from thesurface into a single outgoing angle. If the incoming gas particles andthe surface have the same temperature, the incident angle and theoutgoing angle with respect to the surface normal are the same. That is,the angle of incidence equals the angle of reflection. A second definingcharacteristic of specular reflection is that incident, normal, andreflected directions are coplanar. If the incoming gas particles and thesurface are not at the same temperature and the reflection is diabatic(i.e. with heat exchange between the gas particles and the surface), theangle of reflection is a function of heat transferred between thesurface and the gas particles.

The degree of specularity of a material may be represented by areflection kernel (such as the Cercignani-Lampis kernel) which isdefined as the probability density function of reflected state of thegas particles per unit volume of the phase space. Details of thereflection kernel are disclosed in “Numerical Analysis of Gas-SurfaceScattering Effect on Thermal Transpiration in the Free MolecularRegime”, Vacuum, Vol. 82, Page 20-29, 2009, and references citedtherein, all of which are hereby incorporated by reference.

Individual hot and cold layers may also be constructed of one or morestructural elements which can comprise structural materials, e.g. ameans for conferring rigidity, thermal conductive material, e.g. a meansfor heat transfer to and from a temperature differential generatingmeans, and atomic reflection material, e.g. means for providing adesirable reflection kernel properties. In some embodiment, individualhot and cold layers may be constructed of layered composites of suchmaterials.

Thus, the choice of materials is and composition is widely variable. Insome embodiments, materials suitable for construction of NMSET orrelated device can include titanium, silicon, steel, and/or iron.Titanium is light weight and possesses a hexagonal crystallinestructure. Interfaces of titanium may be created at orthogonal angleswithout crystalline warping and therefore no stress limit. Materialcosts of titanium are high. Silicon is inexpensive and has wellunderstood properties and processes for machining. The crystallinestructure of silicon is diamond cubic. Steel is cheaper than titanium,possesses a cubic crystalline structure, and is highly resistant togaseous intrusion. Iron is cheaper than steel and has a crystalline formwhich makes it suitable for application in NMSET and related devices.

Exemplary Methods of Manufacturing NMSET or Related Device

According to one embodiment as shown in FIG. 20, a method ofmanufacturing an NMSET or related device comprises: (a) providing asuitable substrate 2001 such as, for example, amorphous silicon,crystalline silicon, ceramic, etc., the substrate preferably having athickness of 500 to 1500 microns; however thinner and thicker substratesare possible; (b) depositing a first layer 2002, a mostly sacrificiallayer, preferably an electrical insulator, such as, for example, silicondioxide, the first layer 2002 preferably having a thickness of 200 nm to50 microns, however thinner and thicker layers are possible.Furthermore, depending on the area of the substrate window 2001 a, it isadvantageous for this layer to have a tunable stress level. For example,for a 1 cm² substrate window 2001 a, successful results have beenachieved with SiO_(x)N_(y) at 60 MPa tensile strength; (c) forming apattern of discrete islands in any suitable shape such as, for example,strip, square, circle from the first layer 2002 by photolithography andetching the first layer 2002; (d) depositing a second layer 2003 overthe discrete islands, the second layer 2003 being an electricalconductor such as, for example, Al, Nb or Zn, preferably having athickness of 5 to 200 nm, however, other thicknesses are contemplated;(e) depositing a third layer 2004 over the second layer 2003, the thirdlayer 2004 being an electrical insulator such as, for example, silicondioxide or the same material used in layer 2002, preferably having thesame thickness as the first layer 2002, however, other thicknesses arecontemplated; (f) partially removing the third layer 2004 and the secondlayer 2003 until the first layer 2002 is exposed; (g) depositing afourth layer 2005, the fourth layer 2005 being an electrical insulatorsuch as, for example, silicon dioxide preferably of the same material as2003, the fourth layer 2005 preferably having a thickness of 3 to 15 nm,thinner is better as long as there are few or no gaps in coverage; (h)depositing a fifth layer 2006, the fifth layer being an electricalconductor such as, for example, Pt, Ni or Cu, and preferably having athickness of 5 to 200 nm, however, other thicknesses are contemplated;(i) depositing a sixth layer 2007, such layer being formed to protectthe front side of the substrate while the backside is being worked on.Such layer can be made of, for example, wax, photoresist, or silicondioxide substrate attached to the fifth layer 2006 via thermal releasetape, the sixth layer 2007 preferably having a thickness of 500 to 1500microns, however, other thicknesses are contemplated; (j) formingthrough holes 2001 a in the substrate 2001 by photolithography andetching the substrate 2001, such that at least one discrete island ofthe first layer 2002 is exposed therein, the through holes 2001 a havingany suitable shape such as, for example, hexagons, squares and circles,the through holes 2001 being arranged in any suitable pattern such as,for example, a hexagonal grid, square grid and a polar grid; (k)removing exposed discrete islands by etching until portions of thefourth layer 2005 there above are exposed; (l) removing exposed portionsof the fourth layer 2005 by etching until portions of the fifth layer2006 there above are exposed; (m) removing exposed portions of the fifthlayer 2006 by etching; (n) partially removing the fourth layer 2005 byetching laterally such that the second layer 2003 and the fifth layer2006 overhang the fourth layer 2005 by 2-10 nm; (o) completely removingthe sixth layer 2007 by thermal release, dissolving or etching. Thesecond layer 2003 and the fifth layer 2006 preferably have a differenceof at least 0.1 eV, at least 1 eV, at least 2 eV or at least 3 eV intheir work-functions.

According to another embodiment as shown in FIG. 21, a method ofmanufacturing an NMSET or related device comprises: (a) providing asuitable substrate 2101 such as, for example, amorphous silicon,crystalline silicon, ceramic, etc., the substrate preferably having athickness of 500 to 1500 microns; however thinner and thicker substratesare possible; (b) depositing a first layer 2102, a mostly sacrificiallayer, preferably an electrical insulator such as, for example, silicondioxide, the first layer 2102 preferably having a thickness of 50 nm to1000 nm; however thinner and thicker layers are possible. Furthermore,depending on the area of the substrate window 2101 a, it is advantageousfor this layer to have a tunable stress level. For example, for a 1 cm²substrate window 2101 a, successful results have been achieved withSiO_(x)N_(y) at 60 MPa tensile strength; (c) depositing a second layer2103 over the first layer 2102, the second layer 2103 being anelectrical conductor such as, for example, Al, Nb or Zn and preferablyhaving a thickness of 5 to 150 nm, however, other thicknesses arecontemplated; (d) depositing a third layer 2104 over the second layer2103, the third layer 2104 being an electrical insulator such as, forexample, silicon dioxide and preferably having a thickness of 5 to 100nm, however, other thicknesses are contemplated, and preferably the samematerial as 2102; (e) depositing a fourth layer 2105 over the thirdlayer 2104, the fourth layer 2105 being an electrical conductor such as,for example, Pt, Ni or Cu and preferably having a thickness of 5-150 nm,however, other thicknesses are contemplated; (f) forming holes throughthe second layer 2103, the third layer 2104 and the fourth layer 2105 byphotolithography and etching, the holes having any suitable shape suchas, for example, strips, squares, circles; (g) partially removing thethird layer 2104 by etching laterally such that the second layer 2103and the fourth layer 2105 overhang the third layer 2104; (h) formingthrough holes 2101 a in the substrate 2101 by photolithography andetching the substrate 2101, such that at least one hole through thesecond layer 2103, the third layer 2104 and the fourth layer 2105overlaps with one through hole 2101 a, the through holes 2101 a havingany suitable shape such as, for example, hexagons, squares and circles,the through holes 2101 being arranged in any suitable pattern such as,for example, a hexagonal grid, square grid and a polar grid; (i)removing portions of the first layer 2102 exposed in the through holes2101 a. The second layer 2103 and the fourth layer 2105 preferably havea difference of at least 0.1 eV, at least 1 eV, at least 2 eV or atleast 3 eV in their work-functions.

While NMSET and related device have been described in detail withreference to specific embodiments thereof, it will be apparent to thoseskilled in the art that various changes and modifications can be made,and equivalents employed, without departing from the scope of theappended claims.

1. An apparatus operable to propel a gas, comprising: at least a firstlayer and a second layer arranged in a stack and means for heatingand/or cooling the first and second layers to form a hot layer and acold layer wherein the cold layer has a lower temperature than the hotlayer; and, at least one through hole in the stack; wherein: a surfaceof each hot layer is exposed in an interior of the through hole; and asurface of each cold layer is exposed in the interior of the throughhole; and wherein: an entire length of the through hole is up to 10times of a mean free path of a gas in which the apparatus is immersedand/or is not greater than 1500 nm.
 2. The apparatus of claim 1, whereinmeans for heating and cooling the first and second layers is a Peltierdevice or a field-enhanced thermionic emission device.
 3. The apparatusof claim 2, wherein the Peltier device or the field-enhanced thermionicemission device is interposed between the first and second layers. 4.The apparatus of claim 1, wherein the hot layer is heated by one or moreresistive heaters, a chemical reaction, and/or radiation.
 5. Theapparatus of claim 1, wherein the through hole has progressively largercross section areas from an upper face to a lower face of the stack; theexposed surface of each cold layer in the interior of the through holeis substantially parallel to a center axis of the through hole; theexposed surface of each hot layer in the interior of the through hole issubstantially perpendicular to the center axis of the through hole. 6.The apparatus of claim 1, wherein each hot layer has a chamfer facinginward and in a first direction, an angle between the chamfer of eachhot layer and a center axis of the through hole being θ₂; each coldlayer has a chamfer facing inward and in a second direction opposed tothe first direction, an angle between the chamfer of each cold layer andthe center axis of the through hole being θ₁; and a sum of θ₁ and θ₂ isfrom 85° to 95°.
 7. The apparatus of claim 6, wherein θ₂ is from 70 to85°.
 8. The apparatus of claim 6, wherein each hot layer has a thicknessof t_(h), each cold layer has a thickness of t_(c), and the ratio oft_(h) to t_(c) is substantially equal to the ratio of cotangent of θ₂ tocotangent of θ₁.
 9. The apparatus of claim 8, wherein t_(c) is greaterthan t_(h).
 10. The apparatus of claim 1, wherein a gap is interposedbetween the hot and cold layers.
 11. The apparatus of claim 10, whereinthe gap comprises spacer elements.
 12. The apparatus of claim 11,wherein the spacer elements comprise piezoelectric material.
 13. Theapparatus of claim 1, wherein the through hole has a uniform size alongits entire length.
 14. The apparatus of claim 13, wherein the throughhole has a cross-sectional shape of a circle, a slit or a comb.
 15. Theapparatus of claim 13, wherein the apparatus has at least 10 throughholes per square centimeter and/or a total perimeter length of all thethrough holes of the apparatus per square centimeter is at least twocentimeters.
 16. An apparatus comprising a series of the apparatus ofclaim 1 wherein the series are arranged such that the hot layers andcold layers form an alternating stack of hot and cold layers, each hotlayer is hotter than the immediately adjacent cold layers, each coldlayer is colder than the immediate adjacent hot layers, and at least onethrough hole is aligned across the stack.
 17. The apparatus of claim 16in which the diameter of the through hole of each member of the seriesis progressively different from an upper face to a lower face of thestack.
 18. A method of using the apparatus of claim 1 comprisingexposing the apparatus to a gas at an ambient temperature and pressureand activating the means of heating and/or cooling alternating layers toform alternating hot and cold layers such that the gas is propelledthrough the through hole.
 19. The method of claim 18 wherein each hotlayer is hotter than the ambient temperature of the gas and each coldlayer is colder than the ambient temperature of the gas.
 20. The methodof claim 18 wherein the mean temperature of all the hot and cold layersis substantially the same as the ambient temperature of the gas.
 21. Amethod of manufacturing the apparatus of claim 1, comprising: running asimulation of an apparatus according to claim 1 having a specificselected starting geometric arrangement of through hole and layers, thesimulation comprising initializing a group of simulated gas particleswith random initial positions and momenta around a simulated apparatus,calculating positions and momenta of these particles after a small timeinterval from the initial positions and momenta using known physicallaws, repeating the calculation through a chosen number of iterations,and analyzing the positions and momenta of the gas particles through thesimulation, modifying the geometric arrangement of the device within adefined search space and running another simulation through a chosennumber of iterations, identifying a geometric arrangement providing moreefficient propulsion of gas particles through a simulated apparatus thanthe starting geometry; manufacturing an apparatus having the identifiedgeometric arrangement.